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<h1>Ring Road and Phantom Traffic Jams</h1>


The microscopic ring-road simulation scenario shows three-lane
vehicular traffic in a 
closed system, symbolized by a ring road  ("Indianopolis").
We simulate two types of vehicles, "cars" (small, color-coded by
speed), and "trucks" 
(bigger and darker). The vehicle types 
are distinguished by the parameters of the
<a href="./IDM.html"> <emph>Intelligent-Driver Model (IDM)</emph> </a>
which is a representative of the class of <emph>car-following models</emph>. 
For simplicity, 
we assume symmetric ("American") lane-changing and lane-usage
    rules, i.e., one can pass also on the right lane, and trucks can
    drive on the left lane whenever their drivers want to do it.
<p>
The dynamics depends essentially on the average vehicle density rho,
    which is 
the main control parameter in closed systems. 
In the simulations, you can vary the density. On increasing the
      density, new vehicles are "dropped at locations, where 
there is sufficiently space. On decreasing the density, 
arbitrarily selected vehicles are
      just removed.
The following density ranges
    depend on the number and distibution of trucks and can vary from
    simulation to simulation.
<ul>
<li>
 Density rho < 8 vehicles/km/lane:
    Free traffic. Only in very rare cases cars are blocked by two
	parallel-driving trucks.
<li>
rho = 8..15 veh./km/lane: Queues of vehicles
    behind trucks become more frequently
<li>
 rho = 15..25 veh./km/lane: Traffic becomes so dense that, on average,
 also	car-drivers drive more slowly than the maximum speed of
	trucks.
Therefore, there are rarely distinct queues behind trucks. Traffic is
	dense, but yet without congestions.
<li>
 rho = 25..55 veh./km/lane:
the initially nearly homogeneous
traffic flow becomes unstable and small perturbations
(caused by the trucks) develop to one or more "phantom" traffic jams
 emerging "out of
	nothing"! Notice that the stop-and go waves propagate 
<i>against</i> the driving direction.
<li>
rho>50 veh./km/lane: Several regions with
    standing traffic separated by regions where vehicles move slowly.
</ul>

<h2> Feedback Mechanism for Traffic Jams </h2>

Assume that one car brakes a little bit (initial perturbation).
As a consequence, the driver of the car
behind has to brake as well to 
maintain the safety distance. Because the braking deceleration
is finite, the gap between the two vehicle nevertheless becomes too
low, and the driver of the car behind has to
brake even more to regain the correct safety distance.
As a consequence, the driver of the <i>next</i> vehicle behind has to brake
even more and so on ...
Besides this destabilizing mechanism, the relaxation to a certain
gap-dependent local equilibrium velocity acts as a stabililizing
mechanism.
For sufficiently small (or very large) traffic densities, this latter
effects is dominating and perturbations die out

<h2> Universal properties of Traffic jams </h2>

Such stop-and go waves and other kinds of congested
traffic have remarkably universal features characterized by the
following <i> "Traffic jam constants"</i>:

<ul>
<li> The density waves propagate <i> against </i> the direction of
the traffic flow at a velocity of about 15 km/h which does not
depend on the system size, the
initial or boundary conditions or on the perturbations
<li> For equal external conditions, 
the ouflow of all types of moving downstream fronts of congested
  traffic (per lane) 
is about the same. This includes
stop-and-go waves (this scenario <b>Ring Road</b> and also the <b>On-Ramp
    scenario</b>)
but also dissolving 
queues in city traffic when the traffic light gets green.
</ul>

